Let the length of the shortest piece be x cm. Then, length of the second piece and the third piece are (x + 3) cm and 2x cm respectively.

Since the three lengths are to be cut from a single piece of board of length 91 cm, x cm + (x + 3) cm + 2x cm ≤ 91 cm

⇒ 4x + 3 ≤ 91

⇒ 4x ≤ 91 – 3

⇒ 4x ≤ 88

⇒ 4x/4 ≤ 88/4

⇒ x ≤22 ........(i)

Also, the third piece is at least 5 cm longer than the second piece.

∴2x ≥ (x + 3) + 5

⇒ 2x ≥ x + 8

⇒ x ≥ 8 … (2)

From (1) and (2), we obtain

8≤ x ≤ 22

Thus, the possible length of the shortest board is greater than or equal to 8 cm but less than or equal to 22 cm.